The precise control of dielectric elastomer actuators (DEAs) usually relies on cumbersome power devices to generate continuous and complex control signals, hindering the miniaturization of DEA-based soft robots. To solve the above problem, a Neural Implicit Embedded Pulse Width Modulated (PWM) Controller (NEPC) is proposed to generate multilevel PWM signals to compensate for the rate-dependent viscoelas-ticity and mechanical vibration of DEAs. To this end, we first establish a lumped-parameter dynamic model to characterize the nonlinear dynamic responses of the DEA, which is used to generate data for controller training. Next, the NEPC, composed of three parts: (1) the Neural Implicit Embedded Controller (NEC) module, (2) the PWM generator, and (3) an end-to-end training framework, is developed and trained to generate multilevel PWM signals. Finally, different tracking experiments are conducted to verify the effectiveness of our control method. The experimental results of different frequencies and trajectories demonstrate that the NEPC can eliminate the rate-dependent viscoelasticity and mechanical vibration of DEAs. The maximum tracking error and root mean square error are reduced by 37.39% and 19.57% at 5 Hz, respectively.